Your first step in choosing the right footwear for you is knowing what you will be using it for. Are you going to run a few miles on the treadmill, do you do a little bit of cardio paired with lifting or machine use, or do you head straight to the free weights?
If you are going to be putting in a lot of miles on the treadmill, or any of the other cardio equipment, your best shoe would be the traditional running shoe. Running shoes have additional cushioning in them to absorb shock as your foot hits the ground. However, if you do plan on using your running shoes in other areas of the gym they might restrict your movement as they are not designed for lateral movement.
For those of you with more versatile training programs, I would go with a cross trainer. These shoes will add support, but not too much so that they restrict your lateral movements. However, if you are going to be doing a lot of running, I would not recommend using these shoes. They will pack out a lot quicker then a running shoe, and you may not get enough cushioning from them. Cross trainers are your best bet for an all-around gym shoe, as long as you don't use the treadmill in excess.
People who are doing a lot of lifting will want a weightlifting shoe. The benefits of these shoes are that they have a raised heel, firm sole and usually have a strap on the front of them. These 3 components will help you with your form and help you produce force from the ground. When buying a pair of these shoes you want to feel sturdy in them.
As someone who is training for a half marathon and spends a lot of time in the weight room, I have opted for 2 different shoes. One traditional running shoe and a weightlifting shoe. I do this because I don't get enough support from my weight lifters while running (yes I tried this, no it didn't go well). When I have tried lifting in my running shoes, I feel like I'm going to fall on myself, which would be an unpleasant experience that I would like to avoid. To sum it up, find what works best for your gym activities and your body!